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SECTION IINTRODUCTION
Free-space optics (FSO) is a cost-effective and high-bandwidth technique for transferring broadband services via point to point links. The way in which FSO transceivers operate is more or less the same as fiber optic ones; however, since laser signals are now transferred through the atmosphere, the path loss between the transmitter and the receiver becomes raised due to a plethora of pernicious factors that appear. Weather, propagation distance, scattering, absorption, turbulence, pointing error effects, laser wavelength, and data rates are some of the deterministic and random elements that contribute to the overall performance of an optical wireless link [1],[2].
Even if all the deteriorating factors play a significant role, designers and implementers should particularly take meteorological phenomena into consideration when they intend to deploy a robust FSO network in practice. Fog, snow, and rain cause the scattering of laser signals in the atmosphere. Scattering makes a portion of the light beam traveling from a source deflect away from the intended receiver. Another atmospheric effect under clear weather conditions is the turbulence induced by random changes in the atmospheric refractive index. As a result, random phase and irradiance fluctuations (scintillation) of the optical signals are observed at the receiver [3]. Furthermore, the FSO links also depend on the pointing error performance. Pointing errors occur due to mechanical misalignment or errors in tracking systems. Among all phenomena, fog brings about the greatest repercussions since it is constituted of small water droplets having dimensions near the size of infrared wavelengths. Snow and rain also influence the FSO performance, though their impact is significantly less than that of fog. Note that these weather phenomena rarely occur concurrently, and that helps in studying their effects separately [4],[5].
An efficacious solution to mitigate the impairments on the performance of FSO systems is to employ relay-assisted techniques. In a multi-hop transmission, the total transmission path is divided into smaller distances between relays or hops which suffer from less loss. At each relay, the received optical field is processed and forwarded to the next one. In that way, an effective serial relayed network can provide services at far distances [6]. The proper operation of multi-hop networks requires, however, the satisfaction of connectivity among its nodes. A network is said to be fully connected when a path exists from any node to another. The absence of any path between at least one source-destination pair means that the network is said to be disconnected [7]. A critical metric to characterize connectivity is the isolation probability, defined as the probability that a random node cannot communicate with any other nodes [8].
Connectivity seems to have a critical role in wireless networks since the emergence of possible outages in their operation is more frequent than in wireline systems. As the exploitation of the RF band is the common way to provide telecom services on air, the majority of current connectivity studies deals with the performance of radio, mobile, and wireless sensor networks. Typical studies of this kind include [9] and [10]. In the context of optical wireless networking there appears to be an absence of similar works in the open technical literature mainly because the interest in this specific field is nowadays in season. That was the key motivation for our team to start working on this subject, publishing the first papers in the area of ultraviolet communications (see [11] and [12]). However, connectivity issues are much more challenging in the case of FSO networks which suffer mainly from adverse weather conditions. To the best of the authors' knowledge, there does not exist a detailed analysis, and the present study aims to fill this gap.
The rest of the paper is organized as follows. Section II presents, in brief, the assumptions followed by the FSO network model under examination. It summarizes the fundamental concepts of the node isolation probability assuming that the nodes are distributed according to a realistic point-process distribution. It also describes the basic link budget equation focusing on the attenuation effects induced by the main meteorological phenomena including fog/haze, rain, and snow as well. The minimum transmission range of transceiver nodes under the action of the dominant weather effect on the link is finally derived. In Subsection II.C, we evaluate the number of transceivers for a given path-link in order to achieve reliable performance. We also examine the reverse case, i.e., find the service length assuming a known number of FSO transceivers. In all cases, proper parameter values corresponding to practical systems are taken into account. The analysis is completed by investig